The energy required to charge a parallel plate condenser of plate separtion `d` and plate area of cross-section `A` such that the unifom field between the plates is `E` is

Options

A. `in_(0)E^(2)Ad`
B. `(1)/(2)in_(0)E^(2)Ad`
C. `(1)/(2)in_(0)E^(2)//Ad`
D. `in_(0)E^(2)//Ad`

Answer

B

Explanation

Energy density `u=(1)/(2)in_(0)E^(2)`
Volume of capacitor `V'=Ad`
Energy stored in capacitor
`U=uV'=(1)/(2)in_(0)E^(2)Ad`
OR
`U=(1)/(2)CV^(2)=(1)/(2)(Ain_(0))/(d)V^(2)`
`=(1)/(2)(Ain_(0))/(d)(E//d)^(2)=(1)/(2)in_(0)E^(2)Ad`